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Jeb Bush called for reimposing sanctions "across the board" on North Korea if the test is confirmed

Hillary Clinton touted her work as secretary of state in working toward the U.S.'s foreign policy pivot to Asia

(CNN)Republican 2016 presidential hopefuls labeled North Korea's claim that it carried out its first hydrogen bomb test Tuesday an example of failed U.S. leadership by President Barack Obama and former Secretary of State Hillary Clinton, and called on China for help.

Front-runner Donald Trump and Kentucky Sen. Rand Paul -- candidates who've attacked one another throughout the campaign cycle -- appeared to be in agreement that any strategy to deal with North Korean leader Kim Jong Un would require China's assistance.

"China has total control, believe me, they say they don't, they have total control over North Korea, and China should solve that problem, and if they don't solve the problem, we should make trade very difficult with China," Trump told Fox News' "Fox and Friends," adding South Korea also must play a role.

"We defend the world, we defend so many countries, we get nothing ... South Korea is going to have to start ponying up."

Trump added that Kim is "getting too close to doing something."

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The West has yet to confirm that North Korea tested a hydrogen bomb, let alone whether it was successful.

Paul, who's been criticized by defense hawks for being isolationist, rejected the charge that he was advocating no response.

"What I'm saying is, there are no easy solutions," Paul told CNN's Alisyn Camerota on "New Day," before adding that the U.S. should talk to the other powers in the region.

"The one thing we have in our favor is that socialism is an abysmal failure," Paul added, saying the difference between the capitalism of South Korea and socialism in North Korea is visible from space.

Florida Sen. Marco Rubio focused his response on attacking Obama.

"I have been warning throughout this campaign that North Korea is run by a lunatic who has been expanding his nuclear arsenal while President Obama stood idly by," the Florida Republican said in a statement issued late Tuesday night.

Later in New Hampshire, he told reporters, "We haven't gotten it confirmed, but it's an example of a withdrawn America in the world."

He called for reimposing sanctions "across the board" if the test is confirmed, and said, "We need to be serious if we're going to deal with these challenges."

Clinton, for her part, put out a statement Wednesday "strongly" condemning the apparent nuclear test, calling it "a provocative and dangerous act."

"North Korea must have no doubt that we will take whatever steps are necessary to defend ourselves and our treaty allies, South Korea and Japan," she said, adding that the U.S. and the international community should "immediately impose additional sanctions against North Koreans."

Clinton also touted her work as secretary of state in working toward the U.S.'s foreign policy pivot to Asia, including bringing Russia and China on board to assist in leveling sanctions against Pyongyang.

New Jersey Gov. Chris Christie, however, took the alleged North Korean test as an opportunity to knock the current administration.

"This is what weak American leadership gets you. And Americans should be very, very concerned about this, because we have a president right now who has no idea how to lead our country or lead the world," Christie said Wednesday.

Christie added that the U.S. should lead a coalition "that tells North Korea that this kind of conduct is just unacceptable" and tied North Korea's brash actions to the Obama administration's negotiated deal with Iran over its nuclear program.

"The fact is that we've allowed North Korea -- while the President's been playing footsie with the Iranians -- we've allowed the North Koreans to get further and further down the nuclear road," Christie added.

"Of course North Korea would conduct a nuclear test after watching Iran willfully violate an agreement they just made without consequence of any kind from this administration," Fiorina posted on Facebook. "North Korea is yet another Hillary Clinton foreign policy failure. America cannot lead from behind."

A magnitude-5.1 seismic event was registered by the U.S. Geological Survey near previous nuclear test sites, but a senior administration official told CNN that it could take days to obtain the necessary scientific data to determine if the test was indeed successful.

Still, Rubio didn't hesitate to hit Clinton over the purported test.

"If this test is confirmed, it will be just the latest example of the failed Obama-Clinton foreign policy," said Rubio. "Our enemies around the world are taking advantage of Obama's weakness. We need new leadership that will stand up to people like Kim Jong Un and ensure our country has the capabilities necessary to keep America safe."

Three out of four of North Korea's nuclear tests -- in 2009, 2013 and now -- have taken place while Obama has been President.

North Korea's televised announcement of a hydrogen bomb test comes just a couple of days after Rubio laid out an address on national security in the 21st century.

He again called North Korea's leader a "lunatic," saying, "There's no other way to describe him. He expands his military while his country starves. He is growing his nuclear arsenal, and building missiles capable of reaching the West coast of the United States."

Rubio also listed China and Russia's growing militaries, Iran, and ISIS, which can often dominate national security discussions, in the foreground of the national security landscape.